How smooth is the drift of the mixed fractional Brownian motion?
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908934043860992 |
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| author | Chigansky, Pavel Kleptsyna, Marina |
| author_facet | Chigansky, Pavel Kleptsyna, Marina |
| contents | The mixed fractional Brownian motion - the sum of independent fractional and standard Brownian motions - is known to be a semimartingale if the Hurst exponent $H$ of its fractional component satisfies $H > 3/4$. The question posed in the title is motivated by recent findings in quantitative finance. In this note, we show that the drift in its Doob-Meyer decomposition has a derivative that is $γ$-Hölder continuous for any $γ< 2H - 3/2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22542 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | How smooth is the drift of the mixed fractional Brownian motion? Chigansky, Pavel Kleptsyna, Marina Probability 60G44, 60G22 The mixed fractional Brownian motion - the sum of independent fractional and standard Brownian motions - is known to be a semimartingale if the Hurst exponent $H$ of its fractional component satisfies $H > 3/4$. The question posed in the title is motivated by recent findings in quantitative finance. In this note, we show that the drift in its Doob-Meyer decomposition has a derivative that is $γ$-Hölder continuous for any $γ< 2H - 3/2$. |
| title | How smooth is the drift of the mixed fractional Brownian motion? |
| topic | Probability 60G44, 60G22 |
| url | https://arxiv.org/abs/2511.22542 |